An Exact Solution to the Yukawa System in Four Dimensions

TL;DR

This paper presents an exact, closed-form solution to the four-dimensional scalar Yukawa system, establishing a theorem on the initial value problem and extending the method to related systems, with insights into the quantum case.

Contribution

Provides the first exact solution to the four-dimensional Yukawa system and generalizes the approach to related interacting systems.

Findings

Exact solution to the scalar Yukawa system in four dimensions

Proved a theorem on the initial value problem for this system

Comments on the quantum version of the problem

Abstract

An exact, closed form solution to the scalar Yukawa system in four dimensions is presented. The formalism is used to state and prove a theorem on the initial value problem. The method also works for a general, iso-vector form of the interacting system. We close with some comments on the quantum version of this problem.